A teacher wonders, "Since when do collapsible compasses copy lengths?" Suggesting
that Euclid may have posited this basic ability early among his propositions -- for the
purposes of simplifying more interesting constructions -- Doctor Peterson then goes
on to discuss the pedagogical pros and cons of compass quality, reliance, and over-reliance.

QBasic measures angles clockwise from north, while mathematicians measure
them counterclockwise from east. How can I convert QBasic's angle
measures to mathematical ones? Also, do negative angles exist?

What is the formal definition of 'opposite sides' of a polygon? Does a
regular pentagon have opposite sides? Does a concave polygon have
opposite sides? How can we define it consistent with our intuition?

What is the 'official' definition of 'edge'? Specifically, is an edge
restricted to the intersection of two non-coplanar faces or do two-
dimensional shapes have edges? I'm also curious about a definition of
'face'. How many faces does a two-dimensional shape have?